computes the proposal distribution during the importance sampling step for...

computes the proposal distribution during the importance sampling step for gaussian-mixture filters. Fix many bugs.

matlab/particle/gaussian_mixture_filter_bank.m

+function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPPost,StateWeightsPost] =...
+                gaussian_mixture_filter_bank(ReducedForm,obs,StateMu,StateSqrtP,StateWeights,...
+                                                                StructuralShocksMu,StructuralShocksSqrtP,StructuralShocksWeights,...
+                                                                ObservationShocksMu,ObservationShocksSqrtP,ObservationShocksWeights,...
+                                                                H,H_lower_triangular_cholesky,normfactO,DynareOptions) 
+%
+% Computes the proposal with a gaussian approximation for importance
+% sampling 
+% This proposal is a gaussian distribution calculated à la Kalman 
+%
+% INPUTS
+%    reduced_form_model     [structure] Matlab's structure describing the reduced form model.
+%                                       reduced_form_model.measurement.H   [double]   (pp x pp) variance matrix of measurement errors.
+%                                       reduced_form_model.state.Q         [double]   (qq x qq) variance matrix of state errors.
+%                                       reduced_form_model.state.dr        [structure] output of resol.m.
+%    Y                      [double]    pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
+%
+% OUTPUTS
+%    LIK        [double]    scalar, likelihood
+%    lik        [double]    vector, density of observations in each period.
+%
+% REFERENCES
+%
+% NOTES
+%   The vector "lik" is used to evaluate the jacobian of the likelihood.
+% Copyright (C) 2009-2012 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
+
+
+
+persistent init_flag2 mf0 mf1 %nodes3 weights3 weights_c3
+persistent number_of_state_variables number_of_observed_variables 
+persistent number_of_structural_innovations 
+
+% Set local state space model (first-order approximation).
+ghx  = ReducedForm.ghx;
+ghu  = ReducedForm.ghu;
+% Set local state space model (second-order approximation).
+ghxx = ReducedForm.ghxx;
+ghuu = ReducedForm.ghuu;
+ghxu = ReducedForm.ghxu;
+
+if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
+    any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
+    any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
+    ghx
+    ghu
+    ghxx
+    ghuu
+    ghxu
+end
+
+constant = ReducedForm.constant;
+state_variables_steady_state = ReducedForm.state_variables_steady_state;
+
+% Set persistent variables.
+if isempty(init_flag2)
+    mf0 = ReducedForm.mf0;
+    mf1 = ReducedForm.mf1;
+    number_of_state_variables = length(mf0);
+    number_of_observed_variables = length(mf1);
+    number_of_structural_innovations = length(ReducedForm.Q);
+    init_flag2 = 1;
+end
+
+numb = number_of_state_variables+number_of_structural_innovations ;
+
+if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') 
+    [nodes3,weights3] = nwspgr('GQN',numb,DynareOptions.particle.smolyak_accuracy) ;
+    weights_c3 = weights3 ;
+end
+if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature')
+    [nodes3,weights3] = spherical_radial_sigma_points(numb) ;
+    weights_c3 = weights3 ;
+end
+if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
+    [nodes3,weights3,weights_c3] = unscented_sigma_points(numb,DynareOptions) ;    
+end
+
+epsilon =  bsxfun(@plus,StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)',StructuralShocksMu) ;
+StateVectors = bsxfun(@plus,StateSqrtP*nodes3(:,1:number_of_state_variables)',StateMu);
+%ObservationShocks = bsxfun(@plus,ObservationShocksSqrtP*nodes3(:,1+number_of_state_variables+number_of_structural_innovations:number_of_state_variables+number_of_structural_innovations+number_of_observed_variables)',ObservationShocksMu)  ; 
+
+yhat = bsxfun(@minus,StateVectors,state_variables_steady_state) ;
+tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
+PredictedStateMean = tmp(mf0,:)*weights3;
+PredictedObservedMean = tmp(mf1,:)*weights3;
+
+if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature')
+    PredictedStateMean = sum(PredictedStateMean,2) ;
+    PredictedObservedMean = sum(PredictedObservedMean,2) ;
+    dState = (bsxfun(@minus,tmp(mf0,:),PredictedStateMean)').*sqrt(weights3) ;
+    dObserved = (bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)').*sqrt(weights3);
+    PredictedStateVariance = dState'*dState;
+    big_mat = [dObserved  dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ] ;
+    [mat1,mat] = qr2(big_mat) ;
+    mat = mat' ; 
+    clear('mat1');
+    PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables) ;
+    CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables) ;
+    StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables)) ;
+    iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
+    iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot ;
+    sqrdet = 1/sqrt(det(iPredictedObservedVariance)) ;
+    PredictionError = obs - PredictedObservedMean ;
+    StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
+end 
+if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || ...
+   strcmpi(DynareOptions.particle.IS_approximation_method,'unscented') 
+    dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
+    dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
+    PredictedStateVariance = dState*diag(weights_c3)*dState';
+    PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
+    PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
+    sqrdet = sqrt(det(PredictedObservedVariance)) ;
+    iPredictedObservedVariance = inv(PredictedObservedVariance);
+    PredictionError = obs - PredictedObservedMean;
+    KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
+    StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
+    StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
+    StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
+    StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)'; 
+end 
+
+data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;			
+StateMuPrior = PredictedStateMean ;
+StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)' ;
+StateWeightsPrior = StateWeights*StructuralShocksWeights ;			
+StateMuPost = StateVectorMean ;
+StateSqrtPPost = StateVectorVarianceSquareRoot ;
+StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g ;